Exploratory Analysis: FPCA for PFT Pioneering Needleleaf with disturbances between 2015 and 2040

Patches which face a disturbance between the years 2015 and 2040 are the basis for this analysis. As a first step in the exploratory analysis, the data is represented as functions by means of a b-spline basis equivalently as for PFT Tundra, i.e. b-splines of order 6, penalizing the third derivative with a penalization parameter \(\lambda = 1\).

Basis Representation - Pioneering Needleleaf

Figure 1 shows the chosen basis representation for Pioneering Needleleaf.

Figure 1: Smoothed basis representation for PFT Pioneering Needleleaf and all four scenarios.
Figure 1: Smoothed basis representation for PFT Pioneering Needleleaf and all four scenarios.

Principal Component Analysis - Pioneering Needleleaf

To further analyze the data, a FPCA is run for each of the four scenarios and each of the five PFTs separately. Again, let’s take a look at the two principal components for each scenario of PFT Pioneering Needleleaf. Figure 2 shows the principal components.

Figure 2: First two principal components for each scenario for PFT Pioneering Needleleaf
Figure 2: First two principal components for each scenario for PFT Pioneering Needleleaf

For Tundra, we could see huge differences between the Control scenario and the climate scenario. Here however, the principal components for all four scenarios are pretty similar and all reflect the same patterns: high values in the first PC stand for much higher values of above ground carbon than the mean after the 10 first years of the considered time span and vice versa for low values. The second principal component mainly reflects lower values as the mean for higher PC2 scores until a break point and then higher values than the mean, vice versa for lower values of PC2. Note that the time point of the change differs among the scenarios.

With VARIMAX rotation

For a better understanding and an easier interpretation of the principal components, a VARIMAX rotation is applied. This rotation algorithm may reveal more meaningful components of variation in the data (Ramsay et al. (2009)).

Figure 3 shows the VARIMAX rotated first and second principal components for each scenario.

Figure 3: First two principal components for each scenario for PFT Pioneering Needleleaf with VARIMAX rotation.
Figure 3: First two principal components for each scenario for PFT Pioneering Needleleaf with VARIMAX rotation.

Here, the VARIMAX rotation mainly influences the end of the time period in the first principal component and the break point in the second PC.

Cluster detection: PC1 vs. PC2 - Pioneering Needleleaf

In order to detect possible clusters in the data, i.e. the share of above ground carbon may behave in similar ways for several grid points, the two first principal components are plotted against each other for all considered cases: unrotated (Figure 4) and VARIMAX rotated (Figure 5). The color reflects a rough classifying into regions, here continents.

Figure 4: First principal component vs. second principal component for each scenario for PFT Pioneering Needleleaf.
Figure 4: First principal component vs. second principal component for each scenario for PFT Pioneering Needleleaf.

In Figure 4, a light clustering pattern is visible, especially for the more drastic scenarios. The more drastic the scenario, the smaller the PC1 values.

Figure 5: First VARIMAX rotated component vs. second VARIMAX rotated component for each scenario for PFT Pioneering Needleleaf
Figure 5: First VARIMAX rotated component vs. second VARIMAX rotated component for each scenario for PFT Pioneering Needleleaf

Rotation does not lead to a substantial difference in PC scores for Pioneering Needleleaf. This was already indicated in Figure 3 as the PCs hardly change in comparison to the unrotated ones.

Spatial Distribution visualized in world maps

In order to get a better understanding of the spatial component of the data, Figure 6 shows how the portion of above ground carbon from year 0 to 100 after disturbance develop in each grid cell (patch 1).

Figure 6: Spatial distribution of the portion of above ground carbon after distrubance for each scenario for PFT Pioneering Needleleaf.
Figure 6: Spatial distribution of the portion of above ground carbon after distrubance for each scenario for PFT Pioneering Needleleaf.

We can clearly see major differences between the scenarios and the considered regions. The more drastic the warming scenario, the more and earlier Pioneering Needleleaf is present.